How to do Calculus I Homework 

Text:   Calculus, Early Transcendentals, 8th Edition

Authors:  Howard Anton, Irl Bivens, and Stephen Davis

Publisher:  John Wiley & Sons, Inc.
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Read Me 1st :    [ UNDER CONSTRUCTION! ]

	(a)  Before you attempt any of the homework problems at the end
of a section, it is imperative that you read the section from beginning to
end.  You should expect to read the section several times.  The first
reading may be done once over lightly, just to get an overview of the
main definitions, theorem, and propositions.  In subsequent readings you 
should dig more deeply into the details.  Keep this in mind as you wield
your writing utensil on paper: 

		(i)   What mathematical objects really are is codified
precisely via their definitions.  Learn the definitions;

		(ii)  How mathematical varmints behave generally is
captured in the magical incantations that follow words like
Theorem, Proposition, or Lemma.  These may assume a
variety of forms and may involve either complex or compound-complex
sentences.  There is always a hypothesis, which may involve several
conditions or properties, and a conclusion, that may also be
multipart and involve equation(s), inequalities, or other
relations.  ; and

		(iii)  The examples that you will encounter in the text come
in two flavors: illustrative examples, that reveal how the previous
developed theory may be applied in solving a particular type of problem
or even suggest how one might further pursue an interesting idea; and
counter-examples that show the necessity for particular hypotheses in 
describing or predicting the general behavior of mathematical varmints.
Both types are important.

	(b)  After having read the section at least once, read and work
through ALL of the Quick Check Exercises that appear at the
beginning of each exercise set.  [There is one exception to this.  For
11.2 only do QCE's 1 through 3.]  You will find a set of "answers" for
these exercises immediately at the end of the exercise set, not at the end
of the book.  Don't peek until you have done them all and don't use a
calculator.  Take time to write up your solutions with care.  The journey
is important.  Come test time, I do not merely look at what you may claim
as your "final answer".  [ In fact I discourage "boxing" or "circling" of
the end result. ]

	(c)  Once you have completed the Quick Check Exercises, go
on to wrestle with a significant chunk of the problems listed by chapter 
and section in the document Homework Problems.  Don't use a calculator.  
Brief answers to many of the odd numbered problems appear at the back of the 
book.  Essentially all of the problems have an "answer" in the Complete 
Solutions Manual that may be found online at the Math Department's site at 
the following URL:

			http://w3.fiu.edu/math/

To access this document you must have a pdf reader on your
computer, say something like Acrobat Reader, or Ghostview, or 
Xpdf, and you must know an appropriate  name and password. [I will discuss
the matter on the first day of class and will provide reminders on
"class" pages.]  Consequently, you may check up on your solutions. 

	(d)  When checking answers, keep in mind that there may
be alternative, correct solutions, and that things like function
identities permit solutions to appear in many different forms.
Also, be aware that the answers found in the Complete Solutions
Manual are written for instructors.  Consequently many are incomplete.
As a case in point, the "answers" for the requested proofs involving 
epsilon antics from Chapter 2 merely provide the key inequalities and 
do not have the complete incantations required to deal with issues of 
quantification.  Instructors are expected to know how to fill in these
lacunae, and by the end of the course you should, too.

	(e)  Finally,  some of the problems that have been
assigned indicate by means of a small icon that a graphing utility is
needed for the problem.  This is misleading since, for some, all the
graphing utility is intended to supply is a check on a graph that you are
to sketch by hand.  Here you may use either the answer in the back of the 
book or the Student Solutions Manual or the Complete Solutions Manual
that is online.  [Some of the "technology" exercises at the beginning 
of the text may actually be dealt with by hand later!]

	(f)  In a recent, brief book review by Greg Ross of The Infinite 
Book: A Short Guide to the Boundless, Timeless, and Endless by John
D. Barrow found in the Nanoviews of the September - October 2005 American
Scientist is a wonderful quote attributed to John von Neumann.  It is 
this: "In mathematics you don't understand things.  You just get used to
them."   I think this suggests that waiting until two days prior to
test time to begin programming your own private biocomputer is singularly
unwise.  //
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